Alignment 1: 7.RP.A.3
Not yet tagged
Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer Olympics. He ran the 100 meter race in 9.63 seconds. There are about 3.28 feet in a meter and 5280 feet in a mile. What was Usain Bolt's average speed for the 100 meter race in miles per hour?

This task involves a multi-step conversion between two rates, going from meters per second to miles per hour. In this case, the units coming from the 100 meter race are meters per second and we do not have a good intuition for what this means in miles per hour. Most of us are used to thinking about speeds in terms of miles per hour since the speedometers in our automobiles use these units, so it is good for students to be able to convert between miles per hour and other units for speed that naturally come up.
The first solution shows all units in the calculations and does not make any calculations until the end. The second solution goes step by step and provides an excellent opportunity to discuss rounding error as it is important here to make all calculations (as in the first method) before rounding rather than using the rounded numbers for successive calculations.
In addition to the work on conversion of units, it might be interesting to compare the top speed of Usain Bolt to some familiar animals:
Animal
Top Speed (in mph)
Hippopotamus 19
Kangaroo
Horse
Gazelle
Cheetah
45
47
50
70
Compared to the animals in the table, Usain Bolt can only run faster than the hippopotamus (just barely!). Note that the speed calculated in this problem is the average speed for 100 meters which is a little less than the top speed, but Usain
Bolt's top speed is certainly well less than any of the other animals on the list. For a more creative implementation of this task, the teacher could provide the table of different animal speeds and ask the students how Usain Bolt would fair against them in a race.
The relevant practice standards for this problem are MP2, Reason abstractly and quantitatively, as students move between the context and the calculations, and MP6, Attend to precision, as students must focus on units and the accuracy with which they present their final answer. Note that both the time for the 100 meter race and the conversion from meters to feet are given with three digit, so only three digits should remain in the answer. Also, given the number of steps required to solve this problem, it is well aligned to MP1, Make sense of problems and persevere in solving them.
Given the complexity of the problem, it would not be appropriate for high-stakes summative assessment but would be very appropriate in an instructional setting.
Solution: 1 Table
We can make a table of distances and times and then find the corresponding rate at the end. In this solution, each successive line in the table represents a single unit conversion, either for distance or for time. The method used here first finds how many feet per second Usain Bolt is running and then moves from here to miles per hour.
Usain Bolt traveled 100 meters in 9.63 seconds. 1 meter is 3.28 feet, so 100 meters is 100 × 3.28 = 328 feet.
Usain Bolt traveled 328 feet in 9.63 seconds. This means he traveled 1 foot in
9.63 ÷ 328 = 0.02936
seconds.
5280 × 0.02936 = 155 seconds.
At this speed, Usain Bolt would travel 1 mile in 155 seconds. 1 hour is
1 mile in
155 ÷ 3600 = 0.043056
hours.
60 × 60 = 3600
seconds, so he traveled
At this speed, Usain Bolt would travel 23.2 miles in 1 hour.
We can summarize these steps in a table:

Distance Travelled
100 meters
328 feet
1 foot
1 mile
1 mile
23.2 miles
Time
9.63 seconds
9.63 seconds
0.29 seconds
155 seconds
0.043 hours
1 hour
The last line in the table tells shows that Usain Bolt is running a little over 23 miles per hour.
In this table the measurements of 9.63 seconds and 100 meters are not exact. The other measurement, in these calculations, which is not exact is the 3.28 feet per meters. In a situation like this, all further numbers need to be appropriately rounded. The rounding must come at the end, however, after making all calculations: for example, the 0.29 seconds to run a foot is a rounded number. So in the next step when this is used to find how long it would take Usain Bolt to run one mile, the calculation needs to be done not with 0.29 seconds but with 9.63
328 seconds.
÷
Solution: 2 Unit conversions
We are given that Usain Bolt ran 100 meters in 9.63 seconds. We first determine how many meters per second this is: meters second
Next we use the fact that there are about 3.28 meters per foot to convert the speed to feet per second:
=
=
100
9.63
meters second
× 3.28
100 × 3.28
9.63
feet meter feet second
.
× meters second
Next we convert feet to miles. There are 5280 feet in a mile so this gives:
100meters ÷ 9.63seconds =
=
100 × 3.28
9.63
100 × 3.28
9.63 × 5280 mile miles second
.
× feet second
Finally there are 60 seconds per minute and 60 minutes per hour so this is
60 × 60 = 3600
seconds per hour. Using this we can now convert our original information in terms of meters per second to miles per hour:
=
=
100 × 3.28
miles
3600seconds
100 × 3.28 × 3600
9.63 × 5280 miles hour
.
× miles second
Using a calculator, we find that Usain Bolt's average speed over the 100 meter race was about 23.2 miles per hour.
Note that some of the numbers in this calculation, namely 100, 3600, and 5280 are exact while 3.28 and 9.63 are only approximate. Since the approximate numbers only have 3 significant digits we only report three digits in the final answer.
7.RP How Fast is Usain Bolt?
is licensed by Illustrative Mathematics

7.RP How Fast is Usain Bolt?
is licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License